omg, Metallica was the biggest inspiration to me when I was learning to play guitar (early 90s). I don't really listen to them that much anymore (except for the S&M album sometimes), but I'm trying to remember what songs I listened to the most:
(in no particular order)
Nothing Else Matters
Master of Puppets
Fade to Black
One
My Friend Of Misery
Honorable mention to Frayed EnRAB Of Sanity, Leper Messiah, Enter Sandman, and No Leaf Clover. I also love Whiskey in the Jar-o and Astronomy, even tho they're covers. And the Mercyful Fate medely, too.
And I have to mention that Sonata Arctica's cover of Fade to Black is on par with the original.